On p-adic vector bundles and local systems

Apparaît dans la collection : Tropical Geometry, Berkovich Spaces, Arithmetic D-Modules and p-adic Local Systems

Correspondences between vector bundles on p-adic varieties and local systems arise in the context of p-adic Simpson theory for vanishing Higgs field. I will explain recent contributions to this theory obtained jointly with Lucas Mann. We use Scholze's framework of diamonds to prove a category equivalence on any proper adic space of finite type over Cp relating Cp-local systems with integral models to certain modules under the structure sheaf for the v-topology,